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Guaranteed‐quality triangular mesh generation for domains with curved boundaries
Author(s) -
Boivin Charles,
OllivierGooch Carl
Publication year - 2002
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.542
Subject(s) - boundary (topology) , polygon mesh , discretization , mesh generation , chew's second algorithm , ruppert's algorithm , delaunay triangulation , parametric statistics , mathematics , algorithm , computer science , set (abstract data type) , geometry , finite element method , mathematical analysis , constrained delaunay triangulation , engineering , structural engineering , programming language , statistics
Guaranteed‐quality unstructured meshing algorithms facilitate the development of automatic meshing tools. However, these algorithms require domains discretized using a set of linear segments, leading to numerical errors in domains with curved boundaries. We introduce an extension of Ruppert's Delaunay refinement algorithm to two‐dimensional domains with curved boundaries and prove that the same quality bounds apply with curved boundaries as with straight boundaries. We provide implementation details for two‐dimensional boundary patches such as lines, circular arcs, cubic parametric curves, and interpolated splines. We present guaranteed‐quality triangular meshes generated with curved boundaries, and propose solutions to some problems associated with the use of curved boundaries. Copyright © 2002 John Wiley & Sons, Ltd.